The results of analytical studies are presented in which (1) the SAP IV elastic finite-element (FE) code was used to perform modal analyses for a rectangular structure in vacuo and embedded in different backfill materials; and (2) a series of dynamic and static two-dimensional (2D), plane-strain, FE, structure-medium interaction (SMI) code calculations were performed using the HONDO code. The HONDO code SMI calculations were made to investigate the effect of variations in (1) surface airblast loadings; and (2) constitutive properties of the backfill region around a hypothetical, shallow-buried structure on the transient loading environments experienced by the structure. The model analyses showed that the natural frequencies increased as the quality of the material surrounding the structure increases. They also indicated that the planned SMI calculations would have sufficient frequency response. There was a noticeable reduction in the frequencies at which the structures responded in the HONDO code calculations due to a decrease in stiffness of the soil backfill. A linear elastic single-degree-of-freedom system model based on the predominant natural mode of the embedded structure simulated the response of the structure to the three different airblast loadings only when a 20 to 40 percent of critical damping was applied. The damping is believed to be necessary to account for energy removed from the elastic structure because of radiation into the surrounding media and the hysteretic nature of this media.